D. Direction: Answer the following mixing problem using separation of variables. A typical mixing problem involves a tank of fixed capacity filled with a thoroughly mixed solution of some substance, such as salt. A solution of a given concentration enters the tank at a fixed rate and the mixture, thoroughly stirred, leaves at a fixed rate, which may differ from the entering rate. If y(t) denotes the amount of substance in the tank at a time t, then y'(t) is the rate at which the substance is being added minus the rate at which it is being removed. The mathematical description of this situation often leads to a first-order separable differential equation. Problem: A tank contains 20 kg of salt dissolved in 5000L of water. Brine that contains 0.03 kg of salt per liter of water enters the tank at a rate of 25L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt remains in the tank after half an hour?

) Two chemicals A and B are combined to form a chemical C. The rate of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C. Initially there are 43 grams of A and 10 grams of B, and for each gram of B, 1.6 grams of A is used. It has been observed that 13.25 grams of C is formed in 5 minutes. How much is formed in 40 minutes? What is the limiting amount of C after a long time ? grams of C are formed in 40 minutes grams is the limiting amount of C after a long time

4. help pls

When a vertical beam of light passes through a transparent medium, the rate at which its intensity I decreases is proportional to I(t), where t represents the thickness of the medium (in feet). In clear seawater, the intensity 3 feet below the surface is 25% of the initial intensity I of the incident beam. Find the constant of proportionality k, where dI dt k= In(4) 3 = KI. What is the intensity of the beam 17 feet below the surface? (Give your answer in terms of Io. Round any constants or coefficients to five decimal places.) 0.000761 X